Is the collapse a phase transition?

It is shown that the process of the collapse during quantum measurements is a consequence of the quantum symmetry built in the formalism: there exists a nontrivial group of symmetry under which all possible states are invariant after the measurement of the given observable. On the basis of this fact, the postulate of collapse is derived with purely group theoretical considerations. These are analogous to the ones used in Landau's problem of phase transitions. Some further analogies of the processes of the collapse and the phase transitions are discussed.     

Is there a glass transition in planar vortex systems?

The criteria for the existence of a glass transition in a planar vortex array with quenched disorder are studied. Applying a replica Bethe ansatz, we obtain for self-avoiding vortices the exact quenched average free energy and effective stiffness which is found to be in excellent agreement with recent numerical results for the related random bond dimer model [C. Zeng, P. L. Leath, and T. Hwa, Phys. Rev. Lett. 83, 4860 (1999)] Including a repulsive vortex interaction and a finite vortex persistence length xi, we find that for xi-->0 the system is at all temperatures in a glassy phase; a glass transition exists only for finite xi. Our results indicate that planar vortex arrays in superconducting films are glassy at presumably all temperatures.     

Is there a universality of the helix-coil transition in protein models?

The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular, the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis. Received 8 December 1999     

Is bimodality a sufficient condition for a first-order phase transition existence?

Here we present two explicit counterexamples to the widely spread beliefs about an exclusive role of bimodality as the first-order phase transition signal. On the basis of an exactly solvable statistical model generalizing the statistical multifragmentation model of nuclei, we demonstrate that the bimodal distributions can naturally appear both in infinite and in finite systems without a phase transition. In the first counterexample a bimodal distribution appears in an infinite system at the supercritical temperatures due to the negative values of the surface tension coefficient. In the second counterexample we explicitly demonstrate that a bimodal fragment distribution appears in a finite volume analog of a gaseous phase. In contrast to the statistical multifragmentation model, the developed statistical model corresponds to the compressible nuclear liquid with the tricritical endpoint located at one third of the normal nuclear density. The suggested parameterization of the liquid phase equation of state is consistent with the L. Van Hove axioms of statistical mechanics and it does not lead to an appearance of the nonmonotonic isotherms in the macroscopic mixed phase region which are typical for the classical models of the Van der Waals type. Peculiarly, such a way to account for the nuclear liquid compressibility automatically leads to an appearance of an additional state that in many respects resembles the physical antinuclear matter.     

Is there a c-theorem in four dimensions?

The difficulties of extending Zamolodchikov's c-theorem to dimensions d ≠ 2 are discussed. It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, S^d, when suitably regularized, defines a c-function, which, at least to one loop order, is decreasing along RG trajectories and is stationary at RG fixed points, where it is proportional to the usual conformal anomaly. It is shown that the existence of such a c-function, if it satisfies these properties to all orders, is consistent with the expected behavior of QCD in four dimensions.     

Bimodality as a signal of a liquid-gas phase transition in nuclei?

We use the heavy-ion phase-space exploration model to discuss the origin of the bimodality in charge asymmetry observed in nuclear reactions around the Fermi energy. We show that it may be related to the important angular momentum (spin) transferred into the quasiprojectile before secondary decay. As the spin overcomes the critical value, a sudden opening of decay channels is induced and leads to a bimodal distribution for the charge asymmetry. In the model, it is not assigned to a liquid-gas phase transition but to specific instabilities in nuclei with high spin. Therefore, we propose to use these reactions to study instabilities in rotating nuclear droplets.     

Does sex induce a phase transition?

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.     

Is there a reentrant glass in binary mixtures?

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component occurs only if the ratio alpha of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For alpha approximately 1, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with the two-component mode-coupling theory. For alpha<1, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode-coupling theory.     

Quantum transport in 3D Weyl semimetals: Is there ametal-insulator transition?

We calculate the transport properties of three-dimensional Weyl fermions in a disorderedenvironment. The resulting conductivity depends only on the Fermi energy and thescattering rate. First we study the conductivity at the spectral node for a fixedscattering rate and obtain a continuous transition from an insulator at weak disorder to ametal at stronger disorder. Within the self-consistent Born approximation the scatteringrate depends on the Fermi energy. Then it is crucial that the limits of the conductivityfor a vanishing Fermi energy and a vanishing scattering rate do not commute. As a result,there is also metallic behavior in the phase with vanishing scattering rate and only aquantum critical point remains as an insulating phase. The latter turns out to be acritical fixed point in terms of a renormalization-group flow.     

Is there a "most perfect fluid" consistent with quantum field theory?

It was recently conjectured that the ratio of the shear viscosity to entropy density eta/s for any fluid always exceeds [formula: see text]. A theoretical counterexample to this bound can be constructed from a nonrelativistic gas by increasing the number of species in the fluid while keeping the dynamics essentially independent of the species type. The question of whether the underlying structure of relativistic quantum field theory generically inhibits the realization of such a system and thereby preserves the possibility of a universal bound is considered here. Using rather conservative assumptions, it is shown here that a metastable gas of heavy mesons in a particular controlled regime of QCD provides a realization of the counterexample and is consistent with a well-defined underlying relativistic quantum field theory. Thus, quantum field theory appears to impose no lower bound on eta/s, at least for metastable fluids.     

Is there a Di-Ω State?

Resonating-group method has been applied to calculate the ΩΩ (SIJ = -6,0,0) dibaryon state in theframework of the extended quark-delocalization color-screening model. The mass of the di-Ω is predicted to be about45 MeV lower than the Ω-Ω threshold. The effect of channel coupling due to the tensor force and sensitivity to mesonexchange short-range cutoff radius, ro have also been studied.     

Is there a Di-Ω State?

Resonating-group method has been applied to calculate the ΩΩ (SIJ=-6,0,0) dibaryon state in the framework of the extended quark-delocalization color-screening model. The mass of the di-Ω is predicted to be about 45 MeV lower than the Ω-Ω threshold. The effect of channel coupling due to the tensor force and sensitivity to meson exchange short-range cutoff radius, r₀ have also been studied.     

Are there phase transitions in information space?

The interplay between two basic quantities--quantum communication and information--is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.     

Is a Griffiths phase a prerequisite for colossal magnetoresistance?

Detailed measurements of the magnetic and transport behavior of the two La(1-x)Ca(x)MnO(3) single crystals exhibiting colossal magnetoresistance are summarized. The x=0.21 sample exhibits unusual exponents (delta = 20+/-1, gamma = 1.71+/-0.1, beta = 0.09+/-0.01, T(C) = 182+/-1 K) and, more importantly, a Griffiths phase characterized by an exponent lambda = 0.70+/-0.2. By contrast, the x=0.20 specimen displays Heisenberg model behavior with no evidence of such a phase. Thus while a Griffiths phase accounts for the behavior of La(1-x)Ca(x)MnO(3) near optimal doping, it does not appear to be a prerequisite for colossal magnetoresistance in this system.